## Questions

- A bag contains 3 black balls and 6 white ones. If two balls are drawn from the bag one at a time,find;
- The probability of drawing a black ball and a white ball.
- Without replacement.
- With replacement.

- Drawing two white balls.
- Without replacement.
- With replacement.

- The probability of drawing a black ball and a white ball.
- A cupboard has 7 white cups and 5brown cups all identical in size and shape. There is a blackout in the town and Mrs. Bett has to select three cups one after another without replacing the previous ones.
- Draw a tree diagram for the information
- Calculate the probability that she chooses;
- Two white cups and one brown cup
- Two brown cups and one white cup
- At least one white cup
- three cups of the same colour

- A two digit number is formed from the first four prime numbers.
- Draw the table to show the possible outcomes, if each number can be used only once.
- Calculate the probability that a number chosen from the digit numbers is an even number

- The probability that a boy goes to school by bus is
^{1}/_{3 }and by matatu is ½. If he uses a bus, the probability that he is late to school is^{1}/_{5 }and if he uses a matatu, the probability of being late is^{3}/_{10}. If he uses other means of transport, the probability of being late is^{1}/_{20}- Draw a probability tree diagram to represent this information
- What is the probability that he will be late for school
- What is the probability that he be late for school if he does not use a matatu
- What is the probability that he is not late for school

- One day during inspection in a certain secondary school, it was discovered that there was a probability of
^{2}/_{5 }that a students had shaggy hair, if a student had shaggy hair, there was a probability of ½ that he had torn uniform. But if he had properly combed hair, there was a probability of ¼ that he had a torn uniform. If a student had torn uniform there was a probability of^{4}/_{5 }that he had unpolished shoes. Otherwise there was a probability of^{3}/_{5 }that he had polished shoes.- Represent this information in a probability tree diagram
- Find the probability that:-
- a student had all the three faults
- a students had exactly two faults
- a students had no faults at all

- A shop is stocked with plates which are from two suppliers A and B. They are brought in the ratio of 3:5 respectively. 10% of plates from A are defective and 6% of plates fromB are defective
- In a science class
^{2}/_{3 }of the class are boys and the rest are girls. 80% of the boys and 90% of the girls are right handed and the rest are left handed. The probability that a right handed student will break a test-tube in any session is^{1}/_{10 }and the corresponding for the left handed student is^{3}/_{10}, their probability being independent of the student sex .- Complete the probability tree diagram given below
- Using the tree diagram, find the probability that :
- A student chosen from the class is left handed
- A test-tube is broken by a left handed student
- A test-tube is broken by a right handed student
- A test-tube is not broken in any session

- Students who performed well in an examination are to be given an outing. A student has to throw two dice. If he gets a sum greater than 8, he gets a two-days outing, otherwise he gets a one day outing.
- Find the probability that a student gets a two-day outing
- A student who qualifies for a two-day outing throws a die and a coin to decide whether he gets pocket money for the two days or for only one day. If he gets a head and a multiple of 3 he gets pocket money for two days. Find the probability that he is given a two-day outing but given pocket money for only one day
- If a student gets a one-day outing, he throws a die to decide if he gets pocket money or not. If he gets a number greater than 4 he gets the pocket money. Find the probability that:-
- A student gets pocket money for two days
- A student gets pocket money

- A bag contains 6 red beads and 4 white ones. Two beads are selected from the bag at random without replacement.
- Draw a tree diagram to represent the above information.
- Calculate the probability that:
- Both beads are white.
- Both beads are of the same colour.
- At least a red bead is picked.
- The two beads are of different colours.

- A bag contains blue, green and red pens of the same type in the ratio 8:2:5 respectively. A pen is picked at random without replacement and its colour noted.
- Determine the probability that the first pen picked is;
- blue
- either green or red.

- Using a tree diagram, determine the probability that;
- the first two pens picked are both green.
- Only one of the first two pens picked is red.

- Draw the probability space for the possible outcomes when a coin is tossed and a die thrown simultaneously
- Determine the probability of getting a head and an even number.

- Determine the probability that the first pen picked is;
- A box contains five red balls and four black balls all identical. Three balls are drawn without replacement from the box at random;
- Draw a tree diagram to show the situation
- use the tree diagram to find the probability that;
- the balls picked are of the same colour
- more red balls were picked
- at least a black ball was picked
- atmost 1 red ball was picked

- A bag contains 10balls of which 3 are red, 5 are white and 2 are green. Another bag contains 12balls of which 4 are red, 3 are white and 5 are green. A bag is chosen at random and then a ball chosen at random from the bag. Find the probability that the ball so chosen is red
- In a certain science class
^{2}/_{3 }of the class are boys and the rest girls.^{4}/_{5 }of the boys and^{9}/_{10}of the girls are right handed, and the rest are left handed. The probability that a right handed student will break a test-tube in any session is^{1}/_{10 }and the corresponding probability for a left handed student is^{3}/_{10}, these probabilities being independent of the student’s sex.- Represent this information on a tree diagram
- Using the diagram above;
- determine the probability that a student chosen at random form the class is left handed
- determine the probability that a student chosen at random from the class is right handed and will break a test tube in any session

- determine the probability that a test tube is broken in any session

- A box contains 5 red biro pens, 4 black biro pens and 6 green biro pens. If three pens are picked once at random, find the probability that:
- all the biro pens are red
- the biro pens are of the same colour
- the biro pens are one of each colour
- none of the biro pens is red

- The probability that Chebet goes to bed on time ¾ . If she goes to bed on time, the probability that she wakes up on time is
^{5}/_{6}, otherwise her probability of waking up on time is^{1}/_{3}.- Find the probability of Chebet getting to bed on time and waking up on time by use of diagram
- Waking up late

- If Chebet wakes up late, her probability of getting to class on time is 1/5 otherwise, her probability of getting to class on time is 3/5.
- Find the probability of Chebet getting to bed on time and gets to class late
- Getting to bed late and get to class on time

## Answers

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